This project develops new statistical methods for epidemiology with broad applications and also methods as needed for ongoing projects in epidemiology, particularly those related to reproductive studies. The work this year involved seven main projects. (1) Measurements of xenobiotic exposures are often based on levels assayed in blood or urine and the values often fall below the limit of detection of the assay. Good methods for including those censored observations have not been available. We showed that methods developed for survival analysis can be employed and permit confounder adjustment. We illustrated use of our proposed method by applying it to a study of toxic effects on childhood cognitive development in eastern Europe. (2) A second project extended that method to enable analyses of mixtures of chemicals, making use of existing toxic equivalency factors to create a censored toxicity-weighted average for analysis. We applied these approaches to data from the National Health and Nutrition Examination Survey data relating toxic analytes in blood to the presence of a biomarker, anti-nuclear antibodies, for autoimmunity. (3) In another project we have developed improved methods for adjusting for creatinine levels for studying exposures based on urinary levels or adjusting for serum lipid levels when studying lipophilic chemical biomarkers/analytes in serum. Adjustment for errors in exposure assessment secondary to the diluteness of the urine or secondary to the lipid content of the blood can help control bias in estimation of effects of environmental exposures and can improve statistical power to identify effects of environmental exposures. (4) We responded to a paper that was published in Science and drew what we considered to be statistically unsupported conclusions regarding the role of bad luck in carcinogenesis. (5) Collaborative work continues on pooling specimens prior to exposure assessment, where pooling is done within levels of a confounder. (6) Assessment of seasonal effects on the risk of preterm birth applied harmonic analysis via a Cox model to data from the Norwegian Medical Birth Registry, and found little evidence for effect of seasonal exposures after the statistical analysis was done with careful allowance for confounding and measurement errors. (7) In work that is joint with Shanshan Zhao we are developing improved risk prediction models and applying them to data from the Sister Study on incident breast cancer in relation to family structure and disease history.